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We introduce a notion of inexact model of a convex objective function, which allows for errors both in the function and in its gradient. For this situation, a gradient method with an adaptive adjustment of some parameters of the model is…

Optimization and Control · Mathematics 2021-10-12 Fedor S. Stonyakin

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Optimization and Control · Mathematics 2025-07-22 Raghu Bollapragada , Shagun Gupta

Current state-of-the-art multi-objective optimization solvers, by computing gradients of all $m$ objective functions per iteration, produce after $k$ iterations a measure of proximity to critical conditions that is upper-bounded by…

Optimization and Control · Mathematics 2021-05-26 I. F. D. Oliveira , R. H. C. Takahashi

In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

Optimization and Control · Mathematics 2024-10-28 Md Abu Talhamainuddin Ansary

The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…

Numerical Analysis · Mathematics 2024-01-19 Abdeslem Hafid Bentbib , Khalide Jbilou , Ridwane Tahiri

This paper analyzes the convergence rates of the {\it Frank-Wolfe } method for solving convex constrained multiobjective optimization. We establish improved convergence rates under different assumptions on the objective function, the…

Optimization and Control · Mathematics 2024-06-11 Douglas S. Gonçalves , Max L. N. Gonçalves , Jefferson G. Melo

We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We show that the…

Functional Analysis · Mathematics 2018-11-26 Szilárd Csaba László

We consider solving nonconvex composite optimization problems in which the sum of a smooth function and a nonsmooth function is minimized. Many of convergence analyses of proximal gradient-type methods rely on global descent property…

Optimization and Control · Mathematics 2026-04-09 Shotaro Yagishita , Masaru Ito

This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…

Optimization and Control · Mathematics 2025-04-16 Yunier Bello-Cruz , Max L. N. Gonçalves , Jefferson G. Melo , Cassandra Mohr

This paper generalizes the dynamical system proposed by Wang et al. [Siam. J. Sci. Comput., 2021] to multiobjective optimization by investigating a multiobjective accelerated gradient-like flow with asymptotically vanishing normalized…

Optimization and Control · Mathematics 2025-11-25 Yingdong Yin

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Andrei Patrascu

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

Optimization and Control · Mathematics 2024-02-01 Digvijay Boob , Qi Deng , Guanghui Lan

In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…

Optimization and Control · Mathematics 2020-02-26 Julian Rasch , Antonin Chambolle

In this article, we extend our previous work (Applicable Analysis, 2024, pp. 1-25) on the steepest descent method for uncertain multiobjective optimization problems. While that study established local convergence, it did not address global…

Optimization and Control · Mathematics 2025-03-11 Shubham Kumar , Nihar Kumar Mahato , Debdas Ghosh

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…

Optimization and Control · Mathematics 2018-11-13 Aryan Mokhtari , Hamed Hassani , Amin Karbasi

We consider the composite minimization problem with the objective function being the sum of a continuously differentiable and a merely lower semicontinuous and extended-valued function. The proximal gradient method is probably the most…

Optimization and Control · Mathematics 2024-11-20 Christian Kanzow , Leo Lehmann

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

Machine Learning · Statistics 2012-07-26 Alekh Agarwal , Sahand N. Negahban , Martin J. Wainwright

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…

Numerical Analysis · Mathematics 2016-05-13 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato

The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…

Optimization and Control · Mathematics 2026-04-14 Shodai Hamana , Yasushi Narushima

In many modern machine learning applications, structures of underlying mathematical models often yield nonconvex optimization problems. Due to the intractability of nonconvexity, there is a rising need to develop efficient methods for…

Machine Learning · Computer Science 2017-05-16 Qunwei Li , Yi Zhou , Yingbin Liang , Pramod K. Varshney